## Nonaveraging Sequence

N.B. A detailed on-line essay by S. Finch was the starting point for this entry.

An infinite sequence of Positive Integers

is a nonaveraging sequence if it contains no three terms which are in an Arithmetic Progression, so that

for all distinct , , . Wróblewski (1984) showed that

References

Behrend, F. On Sets of Integers which Contain no Three Terms in an Arithmetic Progression.'' Proc. Nat. Acad. Sci. USA 32, 331-332, 1946.

Finch, S. Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/erdos/erdos.html

Gerver, J. L. The Sum of the Reciprocals of a Set of Integers with No Arithmetic Progression of Terms.'' Proc. Amer. Math. Soc. 62, 211-214, 1977.

Gerver, J. L. and Ramsey, L. Sets of Integers with no Long Arithmetic Progressions Generated by the Greedy Algorithm.'' Math. Comput. 33, 1353-1360, 1979.

Guy, R. K. Nonaveraging Sets. Nondividing Sets.'' §C16 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 131-132, 1994.

Wróblewski, J. A Nonaveraging Set of Integers with a Large Sum of Reciprocals.'' Math. Comput. 43, 261-262, 1984.